Solved: Help with Collisions Homework | Calculate Velocity & Mass

[Fabio233]

Homework Statement

hey everybody i got a problem but do not know how to do it, A 2.0 kg frictionless cart is moving at a constant speed of 3.0m/s to the right on a horizontal surface. it then collides with a mass that is at rest. as a result the cart acquires a speed of 1.6m/s. Neglect friction.

Caluclate magnitude and direction of the velocity of the 2.0 kg cart after the collison
Calculate mass of the second cart.

Homework Equations

Im not sure what equations i need to use so that's why i am here.

The Attempt at a Solution

No idea of how to solve please help thanks alot.

 

[rl.bhat]

Homework Statement

hey everybody i got a problem but do not know how to do it, A 2.0 kg frictionless cart is moving at a constant speed of 3.0m/s to the right on a horizontal surface. it then collides with a mass that is at rest. as a result the cart acquires a speed of 1.6m/s. Neglect friction.

Caluclate magnitude and direction of the velocity of the 2.0 kg cart after the collison
Calculate mass of the second cart.
.

Hi Fabio, welcome to PF.

Which final velocity is given? Cart or mass?

 

[tomcue]

Hello,

It seems like you are having trouble with a collision problem involving a frictionless cart and a stationary mass. Don't worry, collisions can be tricky but with the right equations and understanding, you'll be able to solve it.

First, let's start by defining the variables we have in this problem. We have a 2.0 kg cart with an initial velocity of 3.0 m/s to the right (positive direction) and a final velocity of 1.6 m/s after the collision. The mass of the second cart is unknown.

To solve this problem, we can use the conservation of momentum equation, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the first cart before the collision is equal to its momentum after the collision, plus the momentum of the second cart after the collision.

Mathematically, this can be written as:

m1v1 = m1v1' + m2v2'

where m1 is the mass of the first cart, v1 is its initial velocity, v1' is its final velocity after the collision, m2 is the mass of the second cart, and v2' is its final velocity after the collision.

We can solve for v2' by rearranging the equation:

v2' = (m1v1 - m1v1') / m2

Now, since we know all the values except for m2, we can plug them in and solve for the mass of the second cart. This will give us the magnitude and direction of its velocity after the collision.

To determine the direction of the velocity, we can use the conservation of energy equation, which states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In this case, the kinetic energy of the first cart before the collision is equal to its kinetic energy after the collision, plus the kinetic energy of the second cart after the collision.

Mathematically, this can be written as:

(1/2)m1v1^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2

Solving for v2', we get:

v2' = √((m1v1^2 - m1v1'^2) / m2)

Now, we can plug in the values we know and solve for v2'. This